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Multivariate doubly-inflated negative binomial distribution using Gaussian copula. (English) Zbl 1434.62084
Diawara, Norou (ed.), Modern statistical methods for spatial and multivariate data. Cham: Springer. STEAM-H, Sci. Technol. Eng. Agric. Math. Health, 147-161 (2019).
Summary: Studies involving count data appear frequently in the social and natural sciences. Moreover, this data often has a non-normal structure making it difficult to model. Many of these models have inflation points centered around zero and potentially at an additional inflation point. We present a model for doubly-inflated count data using the negative binomial distribution. To maintain the correlation structure, we also use Gaussian copula methods. We provide visuals of the bivariate negative binomial Gaussian copula as well as the bivariate doubly-Inflated negative binomial model. Additionally, we give the expression for the proposed model’s marginal distribution and the $$n$$th order moments. Finally, we present an algorithm for estimating the doubly-inflated negative binomial model’s parameters. A table of the results is given with mean square error (MSE) values for each parameter obtained.
For the entire collection see [Zbl 1426.62011].
##### MSC:
 62H05 Characterization and structure theory for multivariate probability distributions; copulas 62H10 Multivariate distribution of statistics
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